Subgroups — #34033168

Order 18688.

44 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22626929	C₂	1	2	yes	maximal, complemented
2	#22625099	C₂	1	1	yes	maximal, characteristic
3	#17989426	C₄	1	1	yes	characteristic
4	#17989426	C₂²	1	1	yes	characteristic
5	C₃₂×D₇₃	C₄	1	1	yes	characteristic
6	C₁₆×D₇₃	C₈	1	1	yes	characteristic
7	#14556497	C₂×C₄	1	1	yes	characteristic
8	C₃₂×C₇₃	C₈	1	1	yes	characteristic
9	C₈×D₇₃	C₁₆	1	1	yes	characteristic
10	#11924003	C₁₆	1	1	yes	characteristic
11	C₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic
12	C₄×D₇₃	C₃₂	1	1	yes	characteristic
13	C₈×C₇₃	C₂×C₁₆	1	1	yes	characteristic
14	#10596831	C₃₂	1	1	yes	characteristic
15	C₂×D₇₃	C₆₄	1	1	yes	characteristic
16	C₄×C₇₃	C₂×C₃₂	1	1	yes	characteristic
17	Dic₇₃	C₆₄	1	1	yes	characteristic
18	M₂₅₆	—	73	1	no	maximal, Sylow
19	C₂×C₇₃	C₂×C₆₄	1	1	yes	characteristic
20	D₇₃	—	2	1	no	—
21	C₂×C₆₄	—	73	1	no	—
22	C₁₂₈	—	73	2	no	—
23	C₇₃	M₂₅₆	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃₂	—	73	1	no	—
25	C₆₄	—	73	1	no	—
26	C₆₄	—	73	1	no	—
27	C₂×C₁₆	—	73	1	no	—
28	C₃₂	—	73	1	no	—
29	C₃₂	#10596842	1	1	yes	characteristic
30	C₂×C₈	—	73	1	no	—
31	C₁₆	—	73	1	no	—
32	C₁₆	C₂×#10596842	1	1	yes	characteristic
33	C₂×C₄	—	73	1	no	—
34	C₈	—	73	1	no	—
35	C₈	#14556686	1	1	yes	characteristic
36	C₂²	—	73	1	no	—
37	C₄	—	73	1	no	—
38	C₄	#17989694	1	1	yes	characteristic
39	C₂	—	146	1	no	—
40	C₂	#22627034	1	1	yes	characteristic

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #22626929	C₂	semidirect
23. C₇₃	M₂₅₆	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.